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We study the limiting absorption principle and the well-posedness of Maxwellequations with anisotropic sign-changing coefficients in the time-harmonicdomain. The starting point of the analysis is to obtain Cauchy problemsassociated with two Maxwell systems using a change of variables. We then derivea priori estimates for these Cauchy problems using two different approaches.The Fourier approach involves the complementing conditions for the Cauchyproblems associated with two elliptic equations, which were studied in ageneral setting by Agmon, Douglis, and Nirenberg. The variational approachexplores the variational structure of the Cauchy problems of the Maxwellequations. As a result, we obtain general conditions on the coefficients forwhich the limiting absorption principle and the well-posedness hold. Moreover,these {\it new} conditions are of a local character and easy to check. Our workis motivated by and provides general sufficient criteria for the stability ofelectromagnetic fields in the context of negative-index metamaterials.

Limiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients